In Ref. [1]} the CAESAR formalism and the corresponding implementation in the SHERPA plugin were extended to include the phase-space constraints given by SoftDrop grooming with general
parameters \(z_{\text{cut}}\)  and \(\beta \) .
Note
that, as already pointed out in [2]}, differential
distributions computed from Eq. (REF ) at NLL are
discontinuous at \(L=L_z=-\ln z_\text{cut}\) .
A way to cure this behaviour was proposed in Ref. [3]}. However, as this discontinuity is a
subleading (NNLL) effect, we decided to leave it
untouched and checked that the two approaches were in agreement within our theoretical uncertainties.
Furthermore, we note that our resummation is strictly valid in the limit of small
\(z_{\text{cut}}\) , i.e. \(\lambda _\alpha \ll z_{\text{cut}}\ll 1\) . However, for \(\beta =0\)  SoftDrop , finite-\(z_{\text{cut}}\)  corrections are
already present at the (leading) single-logarithmic
accuracy [4]}. For the specific choice of
\(z_{\text{cut}}=0.1\)  adopted in this paper, these corrections have been
studied in [5]} in the context of the groomed jet
mass in dijet processes, and found to have a negligible effect
around one percent.
